The field of the present invention relates to optical reference cavities. In particular, on-chip optical reference cavities are disclosed that exhibit reduced thermorefractive, thermomechanical, or photothermal frequency fluctuations.
The subject matter of the instant application may be related to or enabled by subject matter disclosed in one or more of the following references, each of which is incorporated by reference as if fully set forth herein:                U.S. Pub. No. 2012/0321245 entitled “Silica-on-silicon waveguides and related fabrication methods” published Dec. 20, 2012 in the names of Vahala et al;        U.S. Pub. No. 2012/0320448 entitled “Chip-based frequency comb generator with microwave repetition rate” published Dec. 20, 2012 in the names of Li et al;        U.S. Pat. No. 8,094,987 entitled “Silica-on-silicon waveguides and related fabrication methods” issued Jan. 10, 2012 to Martin Armani;        U.S. Pat. No. 8,045,834 entitled “Silica-on-silicon waveguides and related fabrication methods” issued Oct. 25, 2011 to Painter et al;        U.S. Pub. No. 2009/0285542 entitled “Silica-on-silicon waveguides and related fabrication methods” published Nov. 19, 2009 in the names of Martin Armani et al;        U.S. Pub. No. 2008/0203052 entitled “Method of fabricating a microresonator” published Aug. 28, 2008 in the names of Hossein-Zadeh et al;        U.S. Pub. No. 2004/0179573 entitled “Ultra-high Q micro-resonator and method of fabrication” published Sep. 16, 2004 in the names of Armani et al;        Hansuek Lee, Tong Chen, Jiang Li, Ki Youl Yang, Seokmin Jeon, Oskar Painter, and Kerry J. Vahala, “Chemically etched ultrahigh-Q wedge-resonator on a silicon chip,” Nature Photonics 6, 369 (20 May 2012);        Hansuek Lee, Tong Chen, Jiang Li, Oskar Painter, & Kerry J. Vahala, “Ultra-low-loss optical delay line on a silicon chip,” Nature Communications 3, 867 (29 May 2012);        H. Lee, T. Chen, J. Li, K. Yang, S. Jeon, O. Painter, and K. Vahala, “Ultra-high-Q wedge-resonator on a silicon chip,” arXiv:1112.2196v1 (2011);        J. Li, H. Lee, T. Chen, K. J. Vahala, “Chip-based Frequency Comb with Microwave Repetition Rate,” Frontiers in Optics Meeting, Paper # FWB2 (2011);        H. Lee, T. Chen, J. Li, O. Painter, and K. Vahala, “Ultra-High-Q Micro-Cavity on a Silicon Chip,” Frontiers in Optics Meeting, Paper # FWS2 (2011);        D. K. Armani, T. J. Kippenberg, S. M. Spillane and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421, 925-929 (2003);        S. B. Papp and S. A. Diddams, “Spectral and temporal characterization of a fused-quartz-microresonator optical frequency comb,” Phys. Rev. A. 84, 053833 (2011);        T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-Based Optical Frequency Combs,” Science 332, 555-559 (2011);        Xu et al, “Archimedean spiral cavity ring resonators in silicon as ultra-compact optical comb filters,” Optics Express 18, 1937 (2010);        T. Cannon, L. Yang, and K. J. Vahala, “Dynamical thermal behavior and thermal self-stability of microcavities,” Optics Express 12, 4742 (2004);        Gorodetsky, M. L. & Grudinin, I. S., “Fundamental thermal fluctuations in microspheres,” J. Opt. Soc. Am. B 21, 697-705 (2004);        J. Alnis, A. Schliesser, C. Y. Wang, J. Hofer, T. J. Kippenberg, and T. W. Hänsch, “Thermal-noise limited laser stabilization to a crystalline whispering-gallery-mode resonator,” arXiv:1102.4227v1 (21 Feb. 2011);        Hänsch, T. & Couillaud, B., “Laser frequency stabilization by polarization spectroscopy of a reflecting reference cavity,” Opt. Commun. 35, 441-444 (1980);        R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl Phys B 31(2), 97 (1983);        Eric D. Black, “An introduction to Pound-Drever-Hall laser frequency stabilization,” Am J Phys 69(1), 79 (2001); and        T. Udem, R. Holzwarth and T. W. Hänsch, “Optical frequency metrology,” Nature 416, 233 (2002).        
There exist many devices and techniques in which an optical reference cavity is employed as a frequency reference. One application of particular interest is locking the output frequency of a laser source to an optical resonance frequency of an optical reference cavity 20 (FIG. 1). A variety of schemes have been developed to achieve such locking. Examples include, inter alia, the Hänsch-Couillaud method and the Pound-Drever-Hall method.
Any resonant optical cavity exhibits multiple resonance frequencies that are spaced by the cavity's free spectral range, which is in turn determined by the optical pathlength of the reference cavity over an operational frequency range (equivalently, an operational wavelength range). Over typical operational wavelength ranges (e.g., a few tens or hundreds of nanometers at so-called optical frequencies), the multiple resonance frequencies can be regarded as substantially uniformly spaced in frequency. The linewidth of the resonances of the reference cavity in part determine the utility of the cavity as a frequency reference. Narrower resonant linewidth results in improved precision of frequency measurement or control using the optical reference cavity. The linewidth is mainly determined by the so-called Q-factor of the optical reference cavity, which is in turn determined primarily by the total round-trip optical loss of the reference cavity. Reference cavity Q-factors exceeding 108 and approaching 109 have been demonstrated in optical reference cavities comprising a closed-loop dielectric waveguide formed on a substrate chip; some examples are disclosed in one or more of the preceding references. Such large Q-factors can yield, for example as shown in FIG. 2, frequency linewidths of only a few hundred kHz (or even down to several tens of kHz) at optical frequencies on the order of 2×1014 Hz (i.e., wavelengths around 1500 nm).
Frequency linewidth is not the only determinant of a reference cavity's utility as a frequency reference. Because the optical pathlength of the reference cavity depends on the effective index of the corresponding cavity optical mode and the physical length of the cavity, the multiple resonance frequencies are temperature dependent. Use of an optical reference cavity therefore requires temperature control and stabilization to maintain a sufficiently stable frequency reference. As requirements for the stability of a frequency reference become more and more stringent, however, simple thermal control and stabilization of an optical reference cavity may not be sufficient. Even if the optical reference cavity is maintained at a perfectly invariant bulk temperature, variations or fluctuations in the center frequency of each of the multiple cavity resonances can occur (as in FIG. 3) and can arise from one of several sources. A first source of such fluctuations is the occurrence of localized, transient, statistical fluctuations in the temperature of the reference cavity (i.e., so-called thermorefractive noise). A second source of resonance center frequency fluctuations is the thermal excitation of relatively high frequency (e.g., on the order of 1-100 MHz) vibrational modes of the reference cavity or its supporting structures and coupling of those vibrational modes to the optical modes supported by the reference cavity (i.e., so-called thermomechanical noise). A third source of resonance center frequency fluctuations is the absorption of light circulating in the reference cavity by localized, random defects in the optical material of the reference cavity, which in turn causes localized, intensity dependent heating of the reference cavity (i.e., so-called photothermal noise). These three are major sources of frequency fluctuations in an optical reference cavity realized as a closed-loop dielectric waveguide formed on a substrate chip. Because such on-chip optical reference cavities are desirable for various reasons (e.g., compactness, robustness, manufacturability), it would be desirable to provide on-chip optical reference cavities that exhibit reduced center frequency fluctuations.